Heat flow scaling for mantle convection below a conducting lid: Resolving seemingly inconsistent modeling results regarding continental heat flow

Numerical models of mantle convection below a conducting lid, meant to mimic a continent, have been used 1) to argue that heat flow variations in stable continental regions result principally from lithospheric thickness variations, and 2) to argue that the relationship between lithospheric thickness and continental heat flow is too weak to allow for this. We reconcile these results using a theoretical heat flow scaling which shows that the relationship between heat flow and lid thickness can take on two end-member forms. As the ratio of lid thickness to convecting layer depth increases, the effects of lid thickness variations on heat flow move from weak to strong. Modeling studies that concluded that lithospheric thickness variations could lead to significant continental heat flow variations assumed a convecting layer depth appropriate to upper mantle convection and, thus, maximized the relative thickness of the continental lithosphere, i.e., the conducting lid. Studies that concluded that the relationship is weak assumed whole mantle convection which placed them on the flatter end of the heat flow versus relative lid thickness curve.